The physics of the expansion of the universe is still a poorly studied
subject of the standard cosmological model. This because the concept of
expanding space can not be tested in the laboratory and because ``expansion''
means continuous creation of space, something that leads to several paradoxes.
We re-consider and expand here the discussion of conceptual problems, already
noted in the literature, linked to the expansion of space. In particular we
discuss the problem of the violation of energy conservation for local comoving
volumes, the exact Newtonian form of the Friedmann equations, the receding
velocity of galaxies being greater than the speed of light, and the Hubble law
inside inhomogeneous galaxy distribution. Recent discussion by Kiang, Davis \&
Lineweaver, and Whiting of the non-Doppler nature of the Lemaitre cosmological
redshift in the standard model is just a particular consequence of the
paradoxes mentioned above. The common cause of these paradoxes is the
geometrical description of gravity (general relativity), where there is not a
well defined concept of the energy-momentum tensor for the gravitational field
and hence no energy-momentum conservation for matter plus gravity.Comment: 13 pages, to be published in the Proceedings of the 1st Crisis in
Cosmology Conference, AIP proc. serie
